According to Ritchey:
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What Cleats should I use?
2003 and newer: Ritchey and Shimano pedals will share the same cleats. 2002 and older: The Ritchey pedals are designed to run with Ritchey cleats. The Shimano cleats will clip in but will not perform properly. Your ingress and egress performance will be hampered.
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So I think you need the old Ritchey cleats. I had a pair of those red Ritchey Logic pedals from about 1997 on my MTB, and wanted to change 2 of my bikes to SPDs (1 pair of shoes; MTB and commuter bike). Because of this problem, I ended up buying 2 pairs of new Shimano PD-M520 pedals. Sorry, I don't want to part out the cleats. There are significant differences to the pre-2003 cleats. Here's a pic, Ritchey on the left in silver.

It might be easier just to get newer pedals. Nashbar has two versions of their house brand (made by Wellgo) selling for $25 and $35. These come with brand new, and guaranteed compatible, cleats. Considering the difficulty you are having finding the older model Ritchey cleats and that they will be nearly the price of these pedals if you do find them, go with new.

I know for sure that the 97A cleats were compatible with Shimano pedals, so that would make them as compatible with old Ritchey pedals as Shimano cleats are.
Pretty pathetic that Ritchey won't support a popular product only a few years old.

Can anyone tell me the cleats that come with those pedals? Those work (not well) for the Ritcheys, but they unclip fine which is most important to me. I know Shimano has a few SPD cleat styles so any help would be appreciated, thanks.